Surface Houghton groups are a generalization of Houghton groups to the surface setting. They are defined as groups of asymptotically rigid mapping classes of an infinite-type surface. We will give commensurability and isomorphism classication results for this class of groups. Some time will be spent motivating these groups as “medium” mapping class groups that live somewhere between the world of mapping class groups of finite-type surfaces and those of infinite-type surfaces. This is joint work with Javier Aramayona and Christopher Leininger.